So, we think we may have found the "problem" and it may be more in the UX than in the code. Is it required that the user go out to PayPal, and then return to the order summary page before "Submitting the Order"? Is there any way to complete the order upon returning from PayPal? It seems that many users are not aware of the final step and are leaving the cart after PayPal authorization without finalizing the purchase. Clearly, our client is not happy about this. Please let me know how to finalize the order upon return from PayPal.

So, I've narrowed it down. It turns out that WordFence is causing the popup to display / stay without loading its content. I disabled it and installed your Defender plugin. Rather than spend the day finding the conflict, I'll try out Defender as it will obviously be a more compatible solution for this site.
Thanks so much for your help!

Hello, I have tried the default theme to rule out theme customization, and the overlay is still showing with the spinner. I also setup a login for WPMUDEV that is displayed in the comments inside the Support area of the WPMUDEV Dashboard. Support access has also been granted. I turned on WP_DEBUG, and here are the results:
Strict Standards: Redefining already defined constructor for class Logout_Redirect in /var/www/clients/client1/web1/web/wp-content/plugins/logout-redirect/logout-redirect.php on line 44
Deprecated: Assigning the return value of new by reference is deprecated in /var/www/clients/client1/web1/web/wp-content/plugins/logout-redirect/logout-redirect.php on line 203
Notice: Undefined index: enable_css in /var/www/clients/client1/web1/web/wp-content/plugins/widgets-on-pages/widgets_on_pages.php on line 289
Notice: Trying to get property of non-object in /var/www/clients/client1/web1/web/wp-content/plugins/e-newsletter/email-newsletter-files/builder/class.builder.php on line 368
My next step will be to disable plugins (except Coursepress Pro and Marketpress) and see if I can isolate the problem. I will start with the plugins mentioned above. Those are Logout Redirect, Widgets on Pages, and eNewsletter Pro.